I know how to merge but am thinking specifically on the cupcake wrappers, How do I take outline art, say a butterfly and get the overlapping section from the outline edge of the original cupcake wrapper. I thought if I would group then break apart it might work but my break apart is not working that way

any ideas on the best way to do this. Is there a way to see all the nodes after grouping and delite the nodes individually? Am I making any sense?
I have a large Copam cutter that I have used for vinyl for several years so I am a bit familiar with this type of thin just not seeing what I need.
Any direction would be great help. Thank you
-KimberlyAnn